SymPy Plot: Mouse Support

Now in SVN. Left-click controls rotation, right-click controls zoom. Eventually I want to change it so that right-click controls translation and middle-scroll controls zoom. Right now this does not seem to be possible, because the scroll wheel is not supported by GLUT's mouse handler. I'm looking into it.

Although it has been a while, I never mentioned that basis vectors were added. They still need some tweaking. Also 'q' is added as a quit key.

Right now I'm at a family reunion for the 4th of July holiday. Each summer, my extended family meets for a week to act out our own miniaturized take on Burning Man. FYI, my contract delivery went well on Thursday. However, I'm not quite off the hook yet as I had speculated; it turns out they need additional work.

SymPy 0.4.1 released, with windows installer

This is the first release to include SymPy Plot.

0.4.1 source tarball
0.4.1 windows installer
SymPy homepage
Changelog

PyOpenGL is required for SymPy plotting support. While *nix users should have no problem (apt-get install python-opengl), Windows users will find it difficult, if not impossible, to use PyOpenGL with Python 2.5. I recommend setting up your Python environment as follows:

1. Install Python 2.4.4 to C:\Python24 (the default location)
   I normally like to install all of my programs in C:\Program Files, but unfortunately PyOpenGL depends on the default install path.
2. Install Numeric-23.7.win32-py2.4.exe
3. Install numarray-1.1.1.win32-py2.4.exe
4. Install PyOpenGL-2.0.2.01.py2.4-numpy23.exe
5. Install sympy-0.4.1.win32.exe

6. >>> from sympy import Symbol
   >>> from sympy.modules.graphing import Plot
   >>> x = Symbol('x')
   >>> Plot(x**2, [x, -1, 1, 10])

   

If you get a dll not found error relating to GLUT, obtain glut32.dll and put it in C:\Python24\Lib\site-packages\OpenGL.

SymPy Plot: Now available in SVN

To try it out, check out or update from SVN and look at examples\plotting.py. You'll need to download and setup PyOpenGL for your platform: on ubuntu, apt-get install python-opengl; on windows, you might have luck with the instructions here. So far, I've only tried it on Windows with Python 2.4.



Enjoy, and let me know how it goes!

SymPy Plot: First screenshots

>>> f1 = 0.1+x**2+y**2
>>> f2 = -0.1-x**2-y**2
>>> Plot( f1, f2, [x, -0.75, 0.75, 8], [y, -0.75, 0.75, 8] )

>>> Plot( x*y**3-y*x**3, [x, -1, 1, 20], [y, -1, 1, 20] )

Vision for an extensible visualization tool

In addition to providing standard 2d and 3d function graphing capabilities, the SymPy graphing module will be able to render 2d and 3d geometric entities on the plot, such as lines, vectors, and triangles. While the rendering system will be completely hidden from the casual user who simply wants to plot a few curves or surfaces, advanced users will be able to extend or create new kinds of renderable objects.

A new submodule called sympy.modules.graphing.scene makes this possible by providing a high-level rendering abstraction on top of OpenGL through the Scene class. A Scene handles the boilerplate OpenGL setup and teardown code. It also maintains a list of objects to be rendered, which are represented by objects which implement the Renderable interface. Renderable is a base class providing the render() function, which retrieves the object's primitive representation for rendering. This representation is something that OpenGL can render directly, such as a line list or a tri strip.

For example, consider the Renderable called CartesianCurve, which represents a plane curve in the form y = f(x); when CartesianCurve's render() function is called by a Scene which contains it, it returns a representative list of coordinate pairs, which are then used to render an OpenGL line list. The various other types of plots will be implemented as subclasses of Renderable in the same way. Here are some examples of possible constructor syntax for function plot Renderables:

# y = f(x)
CartesianCurve( x**3, [x, -10, 10, 20] )

# x = f(t), y = f(t)
ParametricCurve( cos(t), sin(t), [t, 0, 2*pi, 32] )

# r = f(theta)
PolarCurve( t, [t, 0, 2*pi, 32] )

# z = f(x, y)
CartesianSurface( x**2+y**2, [x, -1, 1, 5], [y, -1, 1, 5] )

# radius = f(z, theta)
CylindricalShell( 1.0, [z, 0, 1, 2], [t, 0, 2*pi, 32] )
CylindricalShell( t*sqrt(z), [z, 0, 1, 2] )

# radius = f(theta, rho)
SphericalShell( 1.0, [t], [p] )

SymPy Graphing: Starting with PyOpenGL and Feisty

Just a brief update. Progress has been a little slower this week because I've begun working on the new graphing implementation using PyOpenGL and the sample function I wrote about last week. After about a day of tinkering, I had no luck with PyOpenGL on Windows using Python 2.5 (not officially supported yet, apparently). As a result, I've been working in Feisty for the last few days. Unfortunately, I'm having a hard time convincing Feisty to connect to my wpa2-protected wifi, and this is putting a damper on my work flow. Once I get that and a few other nags sorted out, I should be on track.

New direction for SymPy Graphing

In addition to gaining some new perspective on my project this weekend, I've gotten a lot done.



On Friday, I said I wanted to stop supporting matplotlib and to begin focusing on a fresh OpenGL plotting solution. It turns out that matplotlib has better 3d support than I suggested, though it is buggy and still doesn't have everything I need. Fortunately, it turns out we can have it both ways.

I've moved matplotlib 2d plotting support out of modules/graphing.py and into examples/mplot2d.py. I've also added 3d plotting support in examples/mplot3d.py. In accomplishing this, I created a generic sampling function in modules/graphing.py which generates plotting data from a 2d or 3d function over an interval or rectangle:


>>> from sympy.modules.graphing import sample
>>> from sympy import Symbol
>>> x = Symbol('x')
>>> sample(x, (x, 0, 2, 2))
[[0,1,2],[0,1,2]]
>>> sample(x**2, (x, 1, 3, 2))
[[1,2,3], [1,4,9]]


This approach will allow me to support multiple plotting solutions. You should now be able to graph many varieties of functions using matplotlib with the implementations in examples/mplot2d.py and examples/mplot3d.py.


>>> mplot3d(x**2-y**2, (x, -10.0, 10.0, 20), (y, -10.0, 10.0, 20))


The Case for Dropping Matplotlib

My pet motivation for SymPy Graphing is to aid in the creation of interactive calculus visualizations. I want to be able to write an example program which visualizes the normal and tangential components of acceleration along a curve. I want to be able to graph a 3d surface subject to a constraint, perhaps to see only the portion of a surface which falls within a cylindrical boundary. Ondrej mentioned that he would like to be able to plot curvature as the vertex color across a 3d surface. All of these things should be doable. At the same time, SymPy Graphing should be simple and intuitive enough for a non-programming Calc III student to use in Python's interactive mode as a graphing calculator.



In my work on 2d graphing this week, I've utilized matplotlib's pylab interface. Using matplotlib to plot functions from SymPy is pretty straightforward, though I find it clunky and have had many frustrations with it. But as the name implies, matplotlib isn't meant to do much beyond plotting, and has only limited 3d support. I want to do a lot more with SymPy Graphing.

As mentioned above, I'd like to support plotting an arbitrary function as the vertex color across a surface; matplotlib has no mechanism for this. Jason and I have discussed allowing geometric figures and line segments from the geometry module to be drawn through the graphing interface; again, not possible. I'd also like to support interactive rotation, zooming, translation, etc., and possibly someday (outside the scope of GSoC) point-picking; to my knowledge, you cannot do these things in matplotlib.

As I said in my proposal, 3d graphing will be supported through PyOpenGL. In general, this is not a very difficult task (there is a good summary of what it entails at the plot3d website) and this approach will provide the flexibility I want.

The upshot of all this is that I am considering a shift away from matplotlib altogether and toward supporting all graphing, 2d and 3d, through a unified OpenGL interface. I only want to support a fraction of the features of matplotlib. (I'm not trying to banish matplotlib from sympy. In any event, one can easily use matplotlib directly. See the current revision of modules/graphing.py in SVN for an example.) If my project goal was simply to write a SymPy wrapper for matplotlib, I'd be done before the official coding period even begins. To do this right, I'm going to need to get my hands a bit dirtier.

Update:
The 3d support in Matplotlib is better than I'd thought (it can do interactive rotation and scaling). There is a good example here. It also looks like it might be able to do colormaps. I'm looking into it in more depth right now.

Sympy Graphing: Usable Progress, Early Frustrations

Over the weekend, I did a bit of refactoring and added a couple of improvements to sympy/modules/graphing.py (where Fabian had laid a good foundation already). First, I've extended plot() to accept a list of functions in addition to a single function.

from sympy import Symbol
from sympy.modules.graphing import plot
x = Symbol('x')
plot([sqrt(x), log(x), sin(x)], xlabel="x label")


I also added in some code so that functions with discontinuities, such as sqrt where x < 0, are plotted correctly.

f_list = [sqrt(x), sqrt(-x), -sqrt(x), -sqrt(-x)]
plot(f_list, [x, -10.0, 10.0], title="Square Roots")


Unfortunately, this code has hit a snag getting through automated testing. At this point, my best hypothesis is that there is some incompatibility between py.test/doctest and the Tk backend for pylab. I'm going to try a different backend next. Ondrej has opened an issue here.

Google Summer of Code 2007 with SymPy

My project proposal Python as a Symbolic Graphing Calculator with SymPy, PIL, and PyOpenGL has been accepted for Google Summer of Code 2007 under the patronage of the Python Software Foundation!

I'll be working with Ondrej Certik, who started the SymPy project, a CAS for Python. I wanted to contribute to the SymPy project for several reasons. Most importantly, I love Python. Even when I'm coding C#, C++, or Java I usually end up metaprogramming in Python much of the time. Secondly, I am a math student. SymPy is useful to me already, and it's only in version 0.3. I don't think I'm the only one who is unsatisfied with other CAS offerings. I think SymPy has a lot of potential, and I'm glad to be part of the team.

Once I get school over with, this project will have my full attention. I'll be updating the blog with my progress and anything interesting I find along the way. I'll also be writing about other summer projects, including my summer reading. More on this soon.